%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV299^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:37:08 AM UTC 2026
% Result : Theorem 7.37s 3.60s
% Output : Refutation 7.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 18 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 69 ( 8 ~; 0 |; 11 &; 37 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 11 ^; 13 !; 6 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(cNAT_decl,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(cSUCC_decl,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(cZERO_decl,type,
cZERO: ( $i > $o ) > $o ).
thf(cNAT_def,definition,
( cNAT
= ( ^ [A: ( $i > $o ) > $o] :
! [B: ( ( $i > $o ) > $o ) > $o] :
( ( ( B @ cZERO )
& ! [C: ( $i > $o ) > $o] :
( ( B @ C )
=> ( B @ ( cSUCC @ C ) ) ) )
=> ( B @ A ) ) ) ) ).
thf(cSUCC_def,definition,
( cSUCC
= ( ^ [A: ( $i > $o ) > $o,B: $i > $o] :
? [C: $i] :
( ( B @ C )
& ( A
@ ^ [D: $i] :
( ( D != C )
& ( B @ D ) ) ) ) ) ) ).
thf(cZERO_def,definition,
( cZERO
= ( ^ [A: $i > $o] :
~ ? [B: $i] : ( A @ B ) ) ) ).
thf(1,conjecture,
! [A: ( ( $i > $o ) > $o ) > $o] :
( ( ( A @ cZERO )
& ! [B: ( $i > $o ) > $o] :
( ( A @ B )
=> ( A @ ( cSUCC @ B ) ) ) )
=> ! [B: ( $i > $o ) > $o] :
( ( cNAT @ B )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cINDUCTION) ).
thf(2,negated_conjecture,
~ ! [A: ( ( $i > $o ) > $o ) > $o] :
( ( ( A @ cZERO )
& ! [B: ( $i > $o ) > $o] :
( ( A @ B )
=> ( A @ ( cSUCC @ B ) ) ) )
=> ! [B: ( $i > $o ) > $o] :
( ( cNAT @ B )
=> ( A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( ( $i > $o ) > $o ) > $o] :
( ( ( A
@ ^ [B: $i > $o] :
~ ? [C: $i] : ( B @ C ) )
& ! [B: ( $i > $o ) > $o] :
( ( A @ B )
=> ( A
@ ^ [C: $i > $o] :
? [D: $i] :
( ( C @ D )
& ( B
@ ^ [E: $i] :
( ( E != D )
& ( C @ E ) ) ) ) ) ) )
=> ! [B: ( $i > $o ) > $o] :
( ! [C: ( ( $i > $o ) > $o ) > $o] :
( ( ( C
@ ^ [D: $i > $o] :
~ ? [E: $i] : ( D @ E ) )
& ! [D: ( $i > $o ) > $o] :
( ( C @ D )
=> ( C
@ ^ [E: $i > $o] :
? [F: $i] :
( ( E @ F )
& ( D
@ ^ [G: $i] :
( ( G != F )
& ( E @ G ) ) ) ) ) ) )
=> ( C @ B ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV299^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.29/0.31 % Computer : n007.cluster.edu
% 0.29/0.31 % Model : x86_64 x86_64
% 0.29/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.29/0.31 % Memory : 8046.5625MB
% 0.29/0.31 % OS : Linux 6.8.0-71-generic
% 0.29/0.31 % CPULimit : 300
% 0.29/0.31 % WCLimit : 300
% 0.29/0.31 % DateTime : Tue Sep 29 15:30:10 UTC 2026
% 0.29/0.32 % CPUTime :
% 0.29/0.32 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.48/1.15 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.92/1.44 % [INFO] Parsing done (285ms).
% 1.92/1.46 % [INFO] Running in sequential loop mode.
% 3.00/2.07 % [INFO] eprover registered as external prover.
% 3.00/2.08 % [INFO] Scanning for conjecture ...
% 3.29/2.24 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.29/2.28 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.29/2.28 % [INFO] Problem is higher-order (TPTP THF).
% 3.29/2.29 % [INFO] Type checking passed.
% 3.47/2.30 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.99/3.59 % External prover 'e' found a proof!
% 6.99/3.59 % [INFO] Killing All external provers ...
% 6.99/3.59 % Time passed: 3071ms (effective reasoning time: 2122ms)
% 6.99/3.59 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.99/3.60 % Axioms used in derivation (0):
% 6.99/3.60 % No. of inferences in proof: 4
% 7.37/3.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3071 ms resp. 2122 ms w/o parsing
% 7.37/3.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.37/3.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------